How can I solve this: ? lg(2x-3) - lg(4x+2) = lg 3

A property of logarithms is that log(a) + log(b) = log(a*b) so

log(2x-3) + log(4x + 2) = log(3) becomes

 

log[(2x - 3)*(4x + 2)] = log(3)

 

So we must have that (2x - 3)*(4x + 2) = 3

 

Expand the bracketed terms to get 8x² -8x - 6 = 3

 

Subtract 3 from both sides

8x² -8x - 9 = 0

 

Solve for the two values of x using the quadratic formula

x = (8 ± √(64 - 4*8*(-9)) )/(2*8)

 

x ≈  1.673  and x = -0.673